Probability

Did anyone know that over a long period time, if a monkey typed letters at random, it could reproduce the entire work of Shakespeare! Well thats Borel Cantelli Lemma.

Frankly speaking Dr. Onkar Dabeer's course on Probability is the most challenging course I have ever opted in my 18 years as a student. And that even surpasses Rotational Motion in class XI (which I still cant understand) and Engineering Drawing (Nightmare). Its not that the subject is extremely hard or its something extremely abstract. Its just that the very basis of my mathematical background is being questioned? I seriously am starting to doubt whether I ever learnt any maths in all this years. The essential concept of probability (read "Measure Theory") has perhaps astounded me more than anything ever academically.

A set of rational numbers has measure 0. There are certain "nasty" sets like Vitali Sets that are not "measurable". Can u believe it! In a more layman language, there is a collection of things which u can see, you know what they are but you cant measure the quantity.

And the things dont stop there. It gets even more interesting. The central limit theorem. In the long run everything has the same distribution. Its a challenge which I am enjoying (Dont know how much I m able to understand though!).